Warehousing Warehousing are the activities involved in the design - - PowerPoint PPT Presentation

Warehousing

• Warehousing are the activities involved in the design and
• peration of warehouses
• A warehouse is the point in the supply chain where raw

materials, work-in-process (WIP), or finished goods are stored for varying lengths of time.

• Warehouses can be used to add value to a supply chain

in two basic ways:

• 1. Storage. Allows product to be available where and when

its needed.

• 2. Transport Economies. Allows product to be collected,

sorted, and distributed efficiently.

• A public warehouse is a business that rents storage space to
• ther firms on a month-to-month basis. They are often used

by firms to supplement their own private warehouses.

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Types of Warehouses

Warehouse Design Process

• The objectives for warehouse design can include:

– maximizing cube utilization – minimizing total storage costs (including building, equipment, and labor costs) – achieving the required storage throughput – enabling efficient order picking

• In planning a storage layout: either a storage layout is

required to fit into an existing facility, or the facility will be designed to accommodate the storage layout.

Warehouse Design Elements

• The design of a new warehouse includes the

following elements:

• 1. Determining the layout of the storage locations (i.e., the

warehouse layout).

• 2. Determining the number and location of the

input/output (I/O) ports (e.g., the shipping/receiving docks).

• 3. Assigning items (stock-keeping units or SKUs) to storage

locations (slots).

• A typical objective in warehouse design is to

minimize the overall storage cost while providing the required levels of service.

Design Trade-Off

• Warehouse design involves the trade-off between

building and handling costs:

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min Building Costs vs. min Handling Costs max Cube Utilization vs. max Material Accessibility

 

Shape Trade-Off

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vs.

Square shape minimizes perimeter length for a given area, thus minimizing building costs Aspect ratio of 2 (W = 2D)

• min. expected distance

from I/O port to slots, thus minimizing handling costs

W = D I/O W D

W = 2 D I/O W D

Storage Trade-Off

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vs.

Maximizes cube utilization, but minimizes material accessibility Making at least one unit of each item accessible decreases cube utilization

A A B B B C C D E A A B B B C C D E Honeycomb loss

Storage Policies

• A storage policy determines how the slots in a

storage region are assigned to the different SKUs to the stored in the region.

• The differences between storage polices illustrate the

trade-off between minimizing building cost and minimizing handling cost.

• Type of policies:

– Dedicated – Randomized – Class-based

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Dedicated Storage

• Each SKU has a

predetermined number of slots assigned to it.

• Total capacity of the slots

assigned to each SKU must equal the storage space corresponding to the maximum inventory level

• f each individual SKU.
• Minimizes handling cost.
• Maximizes building cost.

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I/O

A B C C

Randomized Storage

• Each SKU can be stored in

any available slot.

• Total capacity of all the

slots must equal the storage space corresponding to the maximum aggregate inventory level of all of the SKUs.

• Maximizes handling cost.
• Minimizes building cost.

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I/O

ABC

Class-based Storage

A BC

I/O

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• Combination of dedicated

and randomized storage, where each SKU is assigned to one of several different storage classes.

• Randomized storage is

used for each SKU within a class, and dedicated storage is used between classes.

• Building and handling

costs between dedicated and randomized.

Individual vs Aggregate SKUs

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Time

1 2 3 4 5 6 7 8 9 10

Inventory

1 2 3 4 5 6 7 8 9 10

A B C ABC

Dedicated Random Class-Based Time A B C ABC AB AC BC 1 4 1 5 5 4 1 2 1 2 3 6 3 4 5 3 4 3 1 8 7 5 4 4 2 4 6 6 2 4 5 5 3 8 5 3 8 6 2 5 7 7 2 5 7 5 3 8 5 3 8 8 3 4 1 8 7 4 5 9 3 3 3 3 10 4 2 3 9 6 7 5 Mi 4 5 3 9 7 7 8

Cube Utilization

• Cube utilization is percentage of the total space (or “cube”)

required for storage actually occupied by items being stored.

• There is usually a trade-off between cube utilization and

material accessibility.

• Bulk storage using block stacking can result in the minimum

cost of storage, but material accessibility is low since only the top of the front stack is accessible.

• Storage racks are used when support and/or material

accessibility is required.

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Honeycomb Loss

• Honeycomb loss, the price paid for accessibility, is the

unusable empty storage space in a lane or stack due to the storage of only a single SKU in each lane or stack

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Height of 5 Levels (Z) Wall Depth of 4 Rows (Y) Cross Aisle Vertical Honeycomb Loss

• f 3 Loads

W i d t h

• f

5 L a n e s ( X ) Down Aisle Horizontal Honeycomb Loss

• f 2 Stacks of 5 Loads Each

Estimating Cube Utilization

• The (3-D) cube utilization for dedicated and randomized

storage can estimated as follows:

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( ) ( )

1 1

item space item space Cube utilization honeycomb down aisle total space item space loss space , dedicated ( ) (3-D) , randomized ( ) , dedicated ( ) (2-D)

N i i N i i

x y z M TS D CU x y z M TS D M x y H TA D CU x

= =

= = + +  ⋅ ⋅ ⋅   =  ⋅ ⋅ ⋅      ⋅ ⋅     = ⋅

∑ ∑

, randomized ( ) M y H TA D         ⋅      

Unit Load

• Unit load: single unit of an item, or multiple units

restricted to maintain their integrity

• Linear dimensions of a unit load:
• Pallet height (5 in.) + load height gives z:

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Depth (stringer length) × Width (deckboard length)

(Stringer length) Depth Width (Deckboard length) x Deckboards Stringer Notch

y × x y × x × z

Cube Utilization for Dedicated Storage

Storage Area at Different Lane Depths Item Space Lanes Total Space Cube Util.

A A A A C C C B B B B B

D = 1 A/2 = 1 12 12 24 50%

A A C C B B B

A/2 = 1

A A C B B

D = 2 12 7 21 57%

A A C B B

A/2 = 1

A C B B

D = 3

A C B

12 5 20 60%

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Total Space/Area

• The total space required, as a function of lane depth D:

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• Eff. lane depth

Total space (3-D): ( ) ( ) 2 2 A A TS D X Y Z xL D yD zH     = ⋅ + ⋅ = ⋅ + ⋅            

eff

( ) Total area (2-D): ( ) ( ) 2 TS D A TA D X Y xL D yD Z   = = ⋅ = ⋅ +    

y A A x A A B B B B B C C C X = xL Y eff = Y+A/2 A Y = yD

Down Aisle Space Storage Area on Opposite Side of the Aisle Honeycomb Loss HCL

Number of Lanes

• Given D, estimated total number of lanes in region:
• Estimated HCL:

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1

, dedicated Number of lanes: ( ) 1 1 , randomized ( 1) 2 2

N i i

M DH L D D H M NH N N DH

=

          = − −        + +       >         

∑

( ) ( ) ( ) ( )

1 1

1 1 1 1 1 1 2 1 1 2 1 2 2

D i

D D D D D i D D D D

− =

  − −   − + − = + = = = =      

∑

Unit Honeycomb Loss: 1 D × A A A A A A Probability:

( )

1 2 D D × −

( )

1 1 D D × − + + = Expected Loss: 3 D = doesn’t occur because slots are used by another SKU

Optimal Lane Depth

• Solving for D in results in:

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( )

*

2 1 Optimal lane depth for randomized storage (in rows): 2 2 A M N D NyH   −   = +    

1 2 3 4 5 6 7 8 9 10 Item Space 24,000 24,000 24,000 24,000 24,000 24,000 24,000 24,000 24,000 24,000 Honeycomb Loss 1,536 3,648 5,376 7,488 9,600 11,712 13,632 15,936 17,472 20,160 Aisle Space 38,304 20,736 14,688 11,808 10,080 8,928 8,064 7,488 6,912 6,624 Total Space 63,840 48,384 44,064 43,296 43,680 44,640 45,696 47,424 48,384 50,784 10,000 20,000 30,000 40,000 50,000 60,000 70,000 Space Lane Depth (in Rows)

( ) dTS D dD =

Max Aggregate Inventory Level

• Usually can determine max inventory level for each SKU:

– Mi = maximum number of units of SKU i

• Since usually don’t know M directly, but can estimate it if

– SKUs’ inventory levels are uncorrelated – Units of each item are either stored or retrieved at a constant rate

• Can add include safety stock for each item, SSi

– For example, if the order size of three SKUs is 50 units and 5 units of each item are held as safety stock

136 1

1 2 2

N i i

M M

=

  = +    

∑

1

1 50 1 3 5 90 2 2 2 2

N i i i i

M SS M SS

=

    −     = + + = + + =                

∑

Steps to Determine Area Requirements

• 1. For randomized storage, assumed to know

N, H, x, y, z, A, and all Mi

– Number of levels, H, depends on building clear height (for block stacking) or shelf spacing – Aisle width, A, depends on type of lift trucks used

• 2. Estimate maximum aggregate inventory level, M
• 3. If D not fixed, estimate optimal land depth, D*
• 4. Estimate number of lanes required, L(D*)
• 5. Determine total 2-D area, TA(D*)

137

Aisle Width Design Parameter

• Typically, A (and sometimes H) is a parameter used to

evaluate different overall design alternatives

• Width depends on type of lift trucks used, a narrower

aisle truck

– reduces area requirements (building costs) – costs more and slows travel and loading time (handling costs)

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9 - 11 ft 7 - 8 ft 8 - 10 ft

Stand-Up CB NA Straddle NA Reach

Example 1: Area Requirements

Units of items A, B, and C are all received and stored as 42 × 36 × 36 in. (y × x × z) pallet loads in a storage region that is along one side of a 10-foot-wide down aisle in the warehouse of a factory. The shipment size received for each item is 31, 62, and 42 pallets, respectively. Pallets can be stored up to three deep and four high in the region.

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36 3' 31 10' 12 3.5' 62 3 3' 42 4 3

A B C

x M A y M D z M H N = = = = = = = = = = =

Example 1: Area Requirements

1. If a dedicated policy is used to store the items, what is the 2- D cube utilization of this storage region?

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1 2 1

31 62 42 ( ) (3) 3 6 4 13 lanes 3(4) 3(4) 3(4) 10 (3) ( ) 3(13) 3.5(3) 605 ft 2 2 31 62 3 3.5 4 4 item space (3) (3) (3)

N i i N i i

M L D L DH A TA xL D yD M x y H CU TA TA

= =

        = = = + + = + + =                     = ⋅ + = ⋅ + =              ⋅ ⋅ + ⋅ ⋅          = = =

∑ ∑

42 4 61% 605      +            =

Example 1: Area Requirements

2. If the shipments of each item are uncorrelated with each

• ther, no safety stock is carried for each item, and retrievals

to the factory floor will occur at a constant rate, what is an estimate the maximum number of units of all items that would ever occur?

141

1

1 31 62 42 1 68 2 2 2 2

N i i

M M

=

  + +   = = = + +        

∑

Example 1: Area Requirements

3. If a randomized policy is used to store the items, what is total 2-D area needed for the storage region?

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2

3 1 1 (3) 2 2 3 1 4 1 68 3(4) 2 2 8 lanes 3(4) 10 (3) ( ) 3(8) 3.5(3) 372 ft 2 2 D D H M NH N L DH N A TA xL D yD = − −       + +       =         − −       + +       = =               = ⋅ + = ⋅ + =        

Example 1: Area Requirements

• 4. What is the optimal lane depth for randomized storage?

5. What is the change in total area associated with using the

• ptimal lane depth as opposed to storing the items three

deep?

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( ) ( )

*

2 10 2(68) 3 1 1 4 2 2 2(3)3.5(4) 2 A M N D NyH     − −     = + = + =        

2 2

4 1 4 1 68 3(4) 2 2 4 (4) 6 lanes 3(4) 10 (4) 3(6) 3.5(4) 342 ft 2 3 (3) 372 ft N D L TA D TA − −       + +       = ⇒ = =             ⇒ = ⋅ + =     = ⇒ =

Example 2: Trailer Loading

How many identical 48 × 42 × 30 in. four-way containers can be shipped in a full truckload? Each container load:

1. Weighs 600 lb 2. Can be stacked up to six high without causing damage from crushing 3. Can be rotated on the trucks with respect to their width and depth.

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Truck Trailer

Cube = 3,332 - 3,968 CFT Max Gross Vehicle Wt = 80,000 lbs = 40 tons Max Payload Wt = 50,000 lbs = 25 tons

Length: 48' - 53' single trailer, 28' double trailer Interior Height: (8'6" - 9'2" = 102" - 110") Width: 8'6" = 102" (8'2" = 98") Max Height: 13'6" = 162" Max of 83 units per TL

X 98/12 = 8.166667 8.166667 ft Y 53 53 ft Z 110/12 = 9.166667 9.166667 ft x [48,42]/12 = 4 3.5 ft y [42,48]/12 = 3.5 4 ft z 30/12 = 2.5 2.5 ft L floor(X/x) = 2 2 D floor(Y/y) = 15 13 H min(6,floor(Z/z)) = 3 3 LDH L*D*H = 90 78 units wt 600 600 lb unit/TL min(LDH, floor(50000/wt)) = 83 78